A relatively short proof of Itô’s formula for SPDEs and its applications

By Nicolai V. Krylov. 2012

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We give a short proof of Itô’s formula for stochastic Hilbert-space valued processes in the setting $$V\subset H\subset V^{*}$$ based on the possibility to lift the stochastic differentials, which are originally in $$V^{*},$$ into $$H.$$ Using this result we also prove the maximum principle for second-order SPDEs in arbitrary domains.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/4d683f07704ed68c44aa4dce05a38bfae4f5c6db